Chapter 6 Exponential and Logarithmic Functions
Chapter 6 Practice Test
Practice Test
- The population of a pod of bottlenose dolphins is modeled by the function[latex]\,A\left(t\right)=8{\left(1.17\right)}^{t},[/latex] where[latex]\,t\,[/latex]is given in years. To the nearest whole number, what will the pod population be after[latex]\,3\,[/latex]years?
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About[latex]\,13\,[/latex]dolphins.
- Find an exponential equation that passes through the points[latex]\,\text{(0, 4)}\,[/latex]and[latex]\,\text{(2, 9)}\text{.}[/latex]
- Drew wants to save $2,500 to go to the next World Cup. To the nearest dollar, how much will he need to invest in an account now with[latex]\,6.25%\,[/latex]APR, compounding daily, in order to reach his goal in[latex]\,4\,[/latex]years?
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[latex]$1,947[/latex]
- An investment account was opened with an initial deposit of $9,600 and earns[latex]\,7.4%\,[/latex]interest, compounded continuously. How much will the account be worth after[latex]\,15\,[/latex]years?
- Graph the function[latex]\,f\left(x\right)=5{\left(0.5\right)}^{-x}\,[/latex]and its reflection across the y-axis on the same axes, and give the y-intercept.
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y-intercept:[latex]\,\left(0,\text{ 5}\right)[/latex]
- The graph shows transformations of the graph of[latex]\,f\left(x\right)={\left(\frac{1}{2}\right)}^{x}.\,[/latex]What is the equation for the transformation?
- Rewrite[latex]\,{\mathrm{log}}_{8.5}\left(614.125\right)=a\,[/latex]as an equivalent exponential equation.
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[latex]{8.5}^{a}=614.125[/latex]
- Rewrite[latex]\,{e}^{\frac{1}{2}}=m\,[/latex]as an equivalent logarithmic equation.
- Solve for[latex]\,x\,[/latex]by converting the logarithmic equation[latex]\,lo{g}_{\frac{1}{7}}\left(x\right)=2\,[/latex]to exponential form.
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[latex]x={\left(\frac{1}{7}\right)}^{2}=\frac{1}{49}[/latex]
- Evaluate[latex]\,\mathrm{log}\left(\text{10,000,000}\right)\,[/latex]without using a calculator.
- Evaluate[latex]\,\mathrm{ln}\left(0.716\right)\,[/latex]using a calculator. Round to the nearest thousandth.
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[latex]\mathrm{ln}\left(0.716\right)\approx -0.334[/latex]
- Graph the function[latex]\,g\left(x\right)=\mathrm{log}\left(12-6x\right)+3.[/latex]
- State the domain, vertical asymptote, and end behavior of the function[latex]\,f\left(x\right)={\mathrm{log}}_{5}\left(39-13x\right)+7.[/latex]
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Domain:[latex]\,x3;\,[/latex]Vertical asymptote:[latex]\,x=3;\,[/latex]End behavior:[latex]\,x\to {3}^{-},f\left(x\right)\to -\infty \,[/latex]and[latex]\,x\to -\infty ,f\left(x\right)\to \infty[/latex]
- Rewrite[latex]\,\mathrm{log}\left(17a\cdot 2b\right)\,[/latex]as a sum.
- Rewrite[latex]\,{\mathrm{log}}_{t}\left(96\right)-{\mathrm{log}}_{t}\left(8\right)\,[/latex]in compact form.
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[latex]{\mathrm{log}}_{t}\left(12\right)[/latex]
- Rewrite[latex]\,{\mathrm{log}}_{8}\left({a}^{\frac{1}{b}}\right)\,[/latex]as a product.
- Use properties of logarithm to expand[latex]\,\mathrm{ln}\